Here’s an interesting problem: My 4001c64 has always had a slight buzz if I’m not touching the strings. Once the strings are touched the buzz goes away. Also, I can eliminate the buzz by touching any metal part of the bass. Now here’s the bizarre part: If I touch the lower part of the horseshoe the buss gets louder, while touching the upper part of the horseshoe eliminates the buzz! This has me totally perplexed as the horseshoe is one continuous piece of metal.

Any guess as to what’s going on.

(I feel like submitting this as a puzzler question for Car Talk.)

Check the ground wire attached to the horseshoe assembly, it may be loose. It's possible that ouching a certain area of the HS may cause the ground wire to make even less contact, increasing the 60 Hz hum.

Also since touching the strings quiets the hum, make sure the ground wire to the tailpiece assembly (usually soldered to the back of the mute pad) is indeed connected at both ends.

Hi, that is a bit perplexing. You didn't say if the problem persists with the pickup selector in bass / treble / both pickup positions. If it does it in all three, make sure you check all the grounds and the solder connections. Just slightly possible you have a cold solder joint as well as any of the other grounds open as previously mentioned. Check those on the bottom of the horseshoe as well and make sure none of the ground wires are frayed either. If its only the horseshoe you can localize checking all of that wiring. Just a thought...

The buzz is isolated to the HS. If I select the neck PU the buzz disappears. The solders appear to be solid. What's the deal with a "cold solder"?

A cold solder is when a solder joint might look to be fine, but the solder may have not heated enough the to properly flow onto and join the wire to the lug of the component. So there could be a gap between the connection of the wire to component. A tiny gap is all is takes to make a bad connection.
Many times, a cold solder joint has too much solder on the joint.

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Throw that piece of firewood where it belongs and get yourself a Rickenbacker!

I wonder whether there was ever a resolution to this?

I'm have EXACTLY the same thing on my 4001C64S. I don't worry about buzzing when my hands are off the strings; that's common and, if I'm not mistaken, it just means your power source isn't very well grounded (touching the strings makes you the ground), nothing to do with the grounding of the instrument itself.

But what is weirder is that when I touch the G-side horseshoe, there's a loud buzz, but not on the E-side. And it goes away when I solo the neck pickup. It's not a big deal, but odd. And odd that at least two of us have the same thing going on.

dcr, that makes me think the G-side shoe is not in good mechanical contact with the common ground the E-side shoe clearly is. If touching a metal surface "injects" noise this is almost always the case.

Here is where I personally have a problem. You have $2,500 bass that is the cream of the Rickenbacker crop and you have a DEFECT. It may not be all that severe, or bothersome to some, but for that kinda of money and product. You should have NO electrical or mechanical issues. They should be repaired under warranty and corrected. That is a lot of money to spend and still have IMO an annoying and sound interfering issue. My first and still favorite 74 4001 had tremendous hum/grounding issues back in the 70-80 period when I was playing at several clubs with flourescent lighting and conflicting voltages. I had to coat the entire pickup section with copper foil to combat it. Eventually bought Bartolin pickups to solve the problem.

I just played another 4001C64S and it has exactly the same buzz. What could account for the consistency of this issue?